TSTP Solution File: BOO031-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : BOO031-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 18:05:55 EDT 2023
% Result : Unsatisfiable 0.85s 0.95s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 20
% Syntax : Number of formulae : 96 ( 88 unt; 8 typ; 0 def)
% Number of atoms : 88 ( 87 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 179 ( 43 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
multiply: ( $i * $i ) > $i ).
tff(decl_23,type,
add: ( $i * $i ) > $i ).
tff(decl_24,type,
inverse: $i > $i ).
tff(decl_25,type,
n1: $i ).
tff(decl_26,type,
n0: $i ).
tff(decl_27,type,
a: $i ).
tff(decl_28,type,
b: $i ).
tff(decl_29,type,
c: $i ).
cnf(property3,axiom,
multiply(add(X1,inverse(X1)),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property3) ).
cnf(additive_inverse,axiom,
add(X1,inverse(X1)) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse) ).
cnf(multiplicative_inverse,axiom,
multiply(X1,inverse(X1)) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse) ).
cnf(l2,axiom,
multiply(X1,add(X2,add(X1,X3))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2) ).
cnf(property3_dual,axiom,
add(multiply(X1,inverse(X1)),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property3_dual) ).
cnf(associativity_of_multiply,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiply) ).
cnf(l1,axiom,
add(X1,multiply(X2,multiply(X1,X3))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
cnf(associativity_of_add,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_add) ).
cnf(l3,axiom,
add(add(multiply(X1,X2),multiply(X2,X3)),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3) ).
cnf(l4,axiom,
multiply(multiply(add(X1,X2),add(X2,X3)),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4) ).
cnf(distributivity,axiom,
add(multiply(X1,X2),add(multiply(X2,X3),multiply(X3,X1))) = multiply(add(X1,X2),multiply(add(X2,X3),add(X3,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity) ).
cnf(prove_multiply_add_property,negated_conjecture,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_multiply_add_property) ).
cnf(c_0_12,axiom,
multiply(add(X1,inverse(X1)),X2) = X2,
property3 ).
cnf(c_0_13,axiom,
add(X1,inverse(X1)) = n1,
additive_inverse ).
cnf(c_0_14,plain,
multiply(n1,X1) = X1,
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
multiply(X1,inverse(X1)) = n0,
multiplicative_inverse ).
cnf(c_0_16,plain,
inverse(n1) = n0,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,axiom,
multiply(X1,add(X2,add(X1,X3))) = X1,
l2 ).
cnf(c_0_18,plain,
add(n1,n0) = n1,
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_19,axiom,
add(multiply(X1,inverse(X1)),X2) = X2,
property3_dual ).
cnf(c_0_20,plain,
add(X1,n1) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_14]) ).
cnf(c_0_21,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity_of_multiply ).
cnf(c_0_22,plain,
add(n0,X1) = X1,
inference(rw,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_23,axiom,
add(X1,multiply(X2,multiply(X1,X3))) = X1,
l1 ).
cnf(c_0_24,plain,
multiply(X1,n1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_20]),c_0_20]) ).
cnf(c_0_25,plain,
multiply(X1,multiply(inverse(X1),X2)) = multiply(n0,X2),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_26,plain,
multiply(n0,add(X1,X2)) = n0,
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_27,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
multiply(n0,inverse(inverse(X1))) = multiply(X1,n0),
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_29,plain,
multiply(n0,X1) = n0,
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_30,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
associativity_of_add ).
cnf(c_0_31,plain,
add(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_14]) ).
cnf(c_0_32,axiom,
add(add(multiply(X1,X2),multiply(X2,X3)),X2) = X2,
l3 ).
cnf(c_0_33,axiom,
multiply(multiply(add(X1,X2),add(X2,X3)),X2) = X2,
l4 ).
cnf(c_0_34,plain,
multiply(X1,n0) = n0,
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
multiply(X1,add(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_36,plain,
add(X1,add(X1,X2)) = add(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
add(multiply(X1,X2),add(multiply(X2,X3),X2)) = X2,
inference(rw,[status(thm)],[c_0_32,c_0_30]) ).
cnf(c_0_38,plain,
multiply(add(X1,X2),multiply(add(X2,X3),X2)) = X2,
inference(rw,[status(thm)],[c_0_33,c_0_21]) ).
cnf(c_0_39,plain,
add(X1,n0) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_34]),c_0_34]) ).
cnf(c_0_40,plain,
multiply(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
cnf(c_0_41,plain,
multiply(X1,add(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_42,plain,
add(X1,multiply(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_14]) ).
cnf(c_0_43,plain,
add(multiply(X1,X2),X2) = X2,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,plain,
add(X1,add(X2,X1)) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_35]),c_0_30]) ).
cnf(c_0_45,plain,
multiply(add(X1,X2),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_46,plain,
multiply(X1,multiply(X2,X1)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_21]) ).
cnf(c_0_47,axiom,
add(multiply(X1,X2),add(multiply(X2,X3),multiply(X3,X1))) = multiply(add(X1,X2),multiply(add(X2,X3),add(X3,X1))),
distributivity ).
cnf(c_0_48,plain,
add(X1,X2) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_41]),c_0_44]) ).
cnf(c_0_49,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_27]),c_0_46]) ).
cnf(c_0_50,plain,
add(X1,add(n1,X2)) = n1,
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_51,plain,
add(X1,add(multiply(X2,X1),X3)) = add(X1,X3),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_52,plain,
add(multiply(X1,X2),multiply(inverse(X2),X1)) = multiply(add(X1,X2),add(inverse(X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_15]),c_0_39]),c_0_13]),c_0_24]),c_0_48]),c_0_49]) ).
cnf(c_0_53,plain,
multiply(X1,add(X2,add(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_41,c_0_30]) ).
cnf(c_0_54,plain,
add(X1,add(inverse(X1),X2)) = add(n1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_13]) ).
cnf(c_0_55,plain,
add(n1,X1) = n1,
inference(spm,[status(thm)],[c_0_22,c_0_50]) ).
cnf(c_0_56,plain,
multiply(X1,multiply(add(X1,X2),X3)) = multiply(X1,X3),
inference(spm,[status(thm)],[c_0_21,c_0_35]) ).
cnf(c_0_57,plain,
multiply(add(X1,X2),add(multiply(X3,X1),X2)) = add(multiply(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_51]),c_0_49]) ).
cnf(c_0_58,plain,
add(multiply(X1,X2),multiply(inverse(X1),X2)) = multiply(add(X2,X1),add(inverse(X1),X2)),
inference(spm,[status(thm)],[c_0_52,c_0_49]) ).
cnf(c_0_59,plain,
multiply(X1,multiply(X2,add(X3,X1))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_42]),c_0_21]) ).
cnf(c_0_60,plain,
add(X1,add(X2,X3)) = add(X2,add(X3,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_48]) ).
cnf(c_0_61,plain,
add(X1,add(inverse(X1),X2)) = n1,
inference(rw,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_62,plain,
multiply(X1,multiply(X2,add(X1,X3))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_46]),c_0_56]) ).
cnf(c_0_63,plain,
multiply(add(X1,X2),add(inverse(X2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_27]),c_0_59]),c_0_35]) ).
cnf(c_0_64,plain,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_40]) ).
cnf(c_0_65,plain,
multiply(X1,inverse(inverse(X1))) = add(X1,inverse(inverse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_15]),c_0_39]),c_0_13]),c_0_24]),c_0_49]),c_0_48]) ).
cnf(c_0_66,plain,
add(X1,multiply(inverse(X1),add(X2,X1))) = add(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_41]),c_0_30]),c_0_31]),c_0_60]),c_0_61]),c_0_24]) ).
cnf(c_0_67,plain,
multiply(inverse(X1),add(X2,X1)) = multiply(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_68,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_35]) ).
cnf(c_0_69,plain,
multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_49]) ).
cnf(c_0_70,plain,
multiply(add(X1,X2),add(X1,add(X2,X3))) = add(X1,X2),
inference(spm,[status(thm)],[c_0_35,c_0_30]) ).
cnf(c_0_71,plain,
add(X1,multiply(inverse(X1),X2)) = add(X2,X1),
inference(rw,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_72,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_68]),c_0_49]),c_0_65]),c_0_68]) ).
cnf(c_0_73,plain,
add(X1,multiply(add(X1,X2),X3)) = multiply(add(X3,X1),add(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_35]),c_0_30]),c_0_36]),c_0_69]),c_0_70]),c_0_48]),c_0_27]),c_0_48]) ).
cnf(c_0_74,plain,
add(multiply(X1,X2),multiply(X1,multiply(X2,X3))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_21]) ).
cnf(c_0_75,plain,
add(inverse(X1),multiply(X1,X2)) = add(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_76,plain,
multiply(inverse(X1),multiply(add(X2,X1),X3)) = multiply(inverse(X1),multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_67]),c_0_21]) ).
cnf(c_0_77,plain,
add(X1,multiply(add(X2,X1),X3)) = multiply(add(X3,X1),add(X2,X1)),
inference(spm,[status(thm)],[c_0_73,c_0_71]) ).
cnf(c_0_78,plain,
add(multiply(X1,X2),multiply(X2,X3)) = multiply(X2,add(multiply(X2,X3),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_64]),c_0_21]),c_0_42]),c_0_60]),c_0_74]),c_0_49]),c_0_41]),c_0_49]) ).
cnf(c_0_79,negated_conjecture,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
prove_multiply_add_property ).
cnf(c_0_80,plain,
multiply(add(X1,X2),add(X3,X2)) = add(multiply(X3,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_72]),c_0_71]),c_0_72]),c_0_48]),c_0_77]) ).
cnf(c_0_81,plain,
multiply(X1,add(multiply(X1,X2),X3)) = multiply(X1,add(X2,multiply(X3,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_27]),c_0_78]),c_0_49]) ).
cnf(c_0_82,negated_conjecture,
add(multiply(a,b),multiply(a,c)) != multiply(a,add(b,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_49]),c_0_49]) ).
cnf(c_0_83,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(multiply(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_78,c_0_49]) ).
cnf(c_0_84,plain,
multiply(X1,add(X2,multiply(X3,X1))) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_80]),c_0_81]) ).
cnf(c_0_85,negated_conjecture,
multiply(a,add(b,multiply(a,c))) != multiply(a,add(b,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_83]),c_0_48]) ).
cnf(c_0_86,plain,
multiply(X1,add(X2,multiply(X1,X3))) = multiply(X1,add(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_42]),c_0_83]),c_0_81]),c_0_49]),c_0_84]) ).
cnf(c_0_87,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86]),c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO031-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.34 % Computer : n008.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Sun Aug 27 08:38:02 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.85/0.95 % Version : CSE_E---1.5
% 0.85/0.95 % Problem : theBenchmark.p
% 0.85/0.95 % Proof found
% 0.85/0.95 % SZS status Theorem for theBenchmark.p
% 0.85/0.95 % SZS output start Proof
% See solution above
% 0.85/0.96 % Total time : 0.389000 s
% 0.85/0.96 % SZS output end Proof
% 0.85/0.96 % Total time : 0.392000 s
%------------------------------------------------------------------------------